Advertisements
Advertisements
प्रश्न
Determine whether the sets of points are collinear?
(a, b + c), (b, c + a) and (c, a + b)
Advertisements
उत्तर
Let the points be A(a, b + c), B(b, c + a) and C(c, a + b)
Area of the triangle = `1/2[(x_1y_2 + x_2y_3 + x_3y_1) - (x_2y_1 + x_3y_2 + x_1y_3)]`
= `1/2["a"("c" + "a") + "b"("a" + "b") + "c"("b" + "c") - "b"("b" + "c") + "c"("c" + "a") + "a"("a" + "b")]`
= `1/2["ac" + "a"^2 + "ab" + "b"^2 + "bc" + "c"^2 - ("b"^2 + "bc" + "c"^2 + "ac" + "a"^2 + "ab")]`
= `1/2 xx 0`
= 0
Since the area of a triangle is 0.
∴ The given points are collinear.
APPEARS IN
संबंधित प्रश्न
An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.
Find the area of a quadrilateral ABCD in which AB = 42 cm, BC = 21 cm, CD = 29 cm, DA =34 cm and diagonal BD =20 cm.
The adjacent sides of a parallelogram ABCD measure 34 cm and 20 cm, and the diagonal AC measures 42 cm. Find the area of the parallelogram.
If the points A(– 3, 9), B(a, b) and C(4, – 5) are collinear and if a + b = 1, then find a and b
Find the area of triangle AGF
Find the area of an equilateral triangle whose perimeter is 180 cm
The semi-perimeter of a triangle having sides 15 cm, 20 cm and 25 cm is
If the side of a rhombus is 10 cm and one diagonal is 16 cm, the area of the rhombus is 96 cm2.
From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are 14 cm, 10 cm and 6 cm. Find the area of the triangle.
A field in the form of a parallelogram has sides 60 m and 40 m and one of its diagonals is 80 m long. Find the area of the parallelogram.
